Since SN2 reaction is more favorable with primary substrates, do allylic primary halides undergo nucleophilic substitution reaction mostly on carbon 1 via "SN2". and in case of secondary allylilc halide would the reaction proceed mostly via SN2 pathway?
You have not provided any conditions for these reactions so it is difficult to assess specifically how you are substituting a hydroxyl group for bromide. If you use water as a solvent, then an SN1 reaction would be likely but liberated HBr would have to be neutralized to avoid acid-catalyzed isomerization or dehydration of the resultant alcohols. If hydroxide is employed as the nucleophile, then elimination is an issue. The primary bromide will likely undergo SN2 displacement with hydroxide to give the primary allylic alcohol. As to the secondary bromide, elimination is a major concern. Ideally, acetate would be a better nucleophile to optimize substitution and repress elimination. Saponification of the acetate esters will liberate the alcohols.
The achiral primary bromide will afford achiral primary alcohol and racemic tertiary alcohol. There is little mechanistic information to be gleaned here. The secondary bromide, if a racemate, will provide racemic products. The secondary bromide is a more interesting case and one that can potentially provide useful information. Ideally, I would employ tosylates as opposed to bromides because they are formed from alcohols that can be prepared as their pure enantiomers. Your secondary bromide R,Z-1 would yield S,Z-2 by SN2 displacement. Syn SN2' addition affords R,E-3 while anti SN2' addition provides S,E-3. In the event that solvolytic conditions are employed, i.e., buffered aqueous acetone, racemic 2 and 3 would be expected barring solvent cage effects. SN1 reactions would proceed via cation transoid-4 and not cisoid-5, which has a syn-pentane interaction.